City Research Online

Abstract

Empirical studies in the social sciences often include covariates that are compositional in nature-vectors of shares that sum to a constant-alongside noncompositional covariates. A common approach to handling compositional data in linear regression is to omit one component to avoid perfect multicollinearity. I demonstrate why these coefficients (along with standard errors and t-statistics) can be highly sensitive to the choice of omitted category. Transforming the compositional data using additive logarithmic ratios (ALR) yields permutation-invariant regressions and permits counterfactual changes in the implied composition that remain within the simplex. Furthermore, I demonstrate that applying a simple scale factor to the ALR coefficients generates the coefficients and standard errors associated with isometric logarithmic ratios (ILR) for the variables of interest. Finally, using log-ratios does not exacerbate inherent problems of multicollinearity associated with compositional data. Economic growth regressions incorporating compositional and noncompositional covariates are used to illustrate.

Publication Type:	Article
Additional Information:	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record will be available online at: https://www.springer.com/journal/180
Publisher Keywords:	Compositional Data, Linear Regression, Log-contrasts, Logarithmic Ratios, Economic Growth Regressions
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HB Economic Theory
Departments:	School of Policy & Global Affairs School of Policy & Global Affairs > Department of Economics
SWORD Depositor:	Symplectic Administrator

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